Answer:
P(S=k) = (1/35)k
8/21
Step-by-step explanation:
P(S=k) is proportional to k
P(S=k) = ck
Total probability is 1
k = 2,3.... 8
Sum of all probabilities =
2c + 3c + 4c + 5c + 6c + 7c + 8c = 1
35c = 1
c = 1/35
P(S=k) = (1/35)k, where k = 2,3,...8
P(1&1):
P(S=2) = 2/35
P(2&2):
P(S=4)/3 = (1/3)(4/35) = 4/105
Because for S=4: (1,3) (2,2) (3,1) and all are equally likely
P(3&3):
P(S=6)/3 = (1/3)(6/35) = 2/35
Because for S=6: (2,4) (3,3) (4,2)
P(4&4):
P(S=8) = 8/35
P(getting doubles = 2/35 + 4/105 + 2/35 + 8/35 = 40/105 = 8/21
Answer:
A) y = 1/3x + 4
B) y = 1/2x - 9
Step-by-step explanation:
A) In order to find this, we must first solve the initial equation for y to get the slope.
-x + 3y = 6
3y = x + 6
y = 1/3x + 2
Now we know the slope to be 1/3 since parallel lines have the same slope. So we take this slope and the point and use point-slope form to find the equation.
y - y1 = m(x - x1)
y - 5 = 1/3(x - 3)
y - 5 = 1/3x - 1
y = 1/3x + 4
B) To find this line, we again have to find the slope of the initial equation by solving for y.
2x + y = -4
y = -2x - 4
Now we know our new slope to be 1/2. This is because perpendicular lines have opposite and reciprocal slopes. We can use this and the point to solve in the same way.
y - y1 = m(x - x1)
y - - 8 = 1/2(x - 2)
y + 8 = 1/2x - 1
y = 1/2x - 9
Answer: 3
x
−
2
y
−
15
=
0
Explanation:
We know that,
the slope of the line
a
x
+
b
y
+
c
=
0
is
m
=
−
a
b
∴
The slope of the line
2
x
+
3
y
=
9
is
m
1
=
−
2
3
∴
The slope of the line perpendicular to
2
x
+
3
y
=
9
is
m
2
=
−
1
m
1
=
−
1
−
2
3
=
3
2
.
Hence,the equn.of line passing through
(
3
,
−
3
)
and
m
2
=
3
2
is
y
−
(
−
3
)
=
3
2
(
x
−
3
)
y
+
3
=
3
2
(
x
−
3
)
⇒
2
y
+
6
=
3
x
−
9
⇒
3
x
−
2
y
−
15
=
0
Note:
The equn.of line passing through
A
(
x
1
,
y
1
)
and
with slope
m
is
y
−
y
1
=
m
(
x
−
x
1
)3
x
−
2
y
−
15
=
0
Explanation:
We know that,
the slope of the line
a
x
+
b
y
+
c
=
0
is
m
=
−
a
b
∴
The slope of the line
2
x
+
3
y
=
9
is
m
1
=
−
2
3
∴
The slope of the line perpendicular to
2
x
+
3
y
=
9
is
m
2
=
−
1
m
1
=
−
1
−
2
3
=
3
2
.
Hence,the equn.of line passing through
(
3
,
−
3
)
and
m
2
=
3
2
is
y
−
(
−
3
)
=
3
2
(
x
−
3
)
y
+
3
=
3
2
(
x
−
3
)
⇒
2
y
+
6
=
3
x
−
9
⇒
3
x
−
2
y
−
15
=
0
Note:
The equn.of line passing through
A
(
x
1
,
y
1
)
and
with slope
m
is
y
−
y
1
=
m
(
x
−
Explanation:
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
rearrange
2
x
+
3
y
=
9
into this form
⇒
3
y
=
−
2
x
+
9
⇒
y
=
−
2
3
x
+
3
←
in slope-intercept form
with slope m
=
−
2
3
Given a line with slope then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
⇒
m
perpendicular
=
−
1
−
2
3
=
3
2
⇒
y
=
3
2
x
+
b
←
is the partial equation
to find b substitute
(
3
,
−
3
)
into the partial equation
−
3
=
9
2
+
b
⇒
b
=
−
6
2
−
9
2
=
−
15
2
⇒
y
=
3
2
x
−
15
2
←
equation of perpendicular lineExplanation:
the equation of a line in
slope-intercept form
is.
∙
x
y
=
m
x
+
b
where m is the slope and b the y-intercept
rearrange
2
x
+
3
y
=
9
into this form
⇒
3
y
=
−
2
x
+
9
⇒
y
=
−
2
3
x
+
3
←
in slope-intercept form
with slope m
=
−
2
3
Given a line with slope then the slope of a line
perpendicular to it is
∙
x
m
perpendicular
=
−
1
m
⇒
m
perpendicular
=
−
1
−
2
3
=
3
2
⇒
y
=
3
2
x
+
b
←
is the partial equation
to find b substitute
(
3
,
−
3
)
into the partial equation
−
3
=
9
2
+
b
⇒
b
=
−
6
2
−
9
2
=
−
15
2
⇒
y
=
3
2
x
−
15
2
←
equation of perpendicular line
<h2>
Step-by-step explanation:</h2><h3>We firstly find the surface area of only one face of the cube:</h3><h3>Sa=a²</h3><h3>Sa=1.2²cm</h3><h3>Sa=1.44cm²</h3>
<h2>
Since the cube has 6 faces we multiply the surface area of one face(144cm²) with 6</h2>
Area(cube)=1.44cm²*6
=8.64cm²
<h2>
Same thing with the prism but we have to find the area of one of his triangle face and rectangle face</h2>
S(triangle)=5mm*4mm*1/2
=10mm²
S(rectangle)=7mm*5mm=35mm²
<h2>
The prism has 2 triangle faces and three rectangle faces so we multiply the area by those numbers and then we add those together to get the final area</h2>
S=10mm²*2+35mm²*3
S=20+105
S=125mm²
<h3><em>
Hope this helped..</em></h3><h3 /><h3><em>Hope this helped..
Brainliest pls..</em></h3>
The answer is 224.7 you got to turn 30% into decimal which is 0.30
then multiply 0.30 and 749 which equals 224.7
